Thermodynamic radii of lanthanide ions derived from metal–ligand complexes stability constants

Here, we describe two sets of thermodynamic ionic radii (r1 and r2) of lanthanide ions derived from the analysis of large set of the stability constants logβ1 and logβ2 of the ML and ML2 complexes of lanthanide ions M (from Ce3+ to Lu3+) with organic ligands (L) in water. It has been demonstrated that the stability constants of two metals Mi and Mj with a given ligand L are related by simple equations logβ1j = r1i/r1j.logβ1i and logβ2j = r2i/r2j.logβ2i which formally correspond to purely electrostatic interactions between spherical cations with organic molecule. Predictive performance of these equations was assessed in fivefold cross-validation procedure. The standard deviation (s) of predictions varies from 0.3 to 1.0 for logβ1 and from 0.4 to 1.2 for logβ2 as a function of the difference of Shannon ionic radii (Δrij) of Mi and Mj: s1 = 0.27 + 4.25Δrij for logβ1 and s2 = 0.39 + 5.16Δrij for logβ2. The new radii r1 and r2 steadily decrease across the Ln series, i.e., they follow the same trend as Shannon effective radii of lanthanide ions. The calculations were performed using experimental data on 2854 logβ1 values for 445 organic ligands and 947 logβ2 values for 156 organic ligands in the complexes with 13 metals.